EU Cohesion Policy and the Equity-Efficiency Trade-Off:

Adding Dynamics to Martin’s Model

Prof. Dr. Dietmar Meyer

Jörg Lackenbauer

April 2005

Andrássy Working Paper Series No. XIII

ISSN 1589-603X Edited by the Professors and Readers of Andrássy Gyula University, Budapest. This series presents ongoing research in a preliminary form. The authors bear the entire responsibility for papers in this series. The views expressed therein are the authors’, and may not reflect the official position of the University. The copyright for all papers appearing in the series remains with the authors.

Author’s adress and affiliation: Prof. Dr. Dietmar Meyer Budapest University of Technology and Economics Stoczek u. 2 St. ép. 413 H-1111 Budapest E-Mail: dmeyer@lucifer.kgt.bme.hu Jörg Lackenbauer Otto-Friedrich University Bamberg Feldkirchenstrasse 21 D-96045 Bamberg E-Mail: joerg.lackenbauer@sowi.uni-bamberg.de © by the author(s)

EU Cohesion Policy and the Equity-Efficiency Trade-Off: Adding Dynamics to Martin’s Model

Dietmar Meyer,Budapest University of Technology and Economics

Jörg Lackenbauer, Otto-Friedrich University of Bamberg

April 27, 2005 Abstract As a result of the combination of endogenous growth theory with the approach of the new economic geography (NEG), several models have been developed to explain spatial income inequality and to formulate possible policy strategies taking into account the equity-efficiency trade-off. The dynamics of this problem should be considered as fundamentally important for the enlargement of the EU, because with respect to the new Member States from Central and Eastern Europe (CEECs), EU cohesion policy is confronted with a double challenge: how can it contribute to attain higher national growth (and therefore convergence towards the EU average income per capita) and at the same time contribute to the decrease of regional disparities within the new Member States? This analysis is particularly appealing against the background of the alleged equity-efficiency trade-off that regional policies often suffer from. After the introduction, in the second part of this paper, some light is shed on this equity-efficiency trade-off in the framework of an overview surveying the theoretical literature on the issue. In the third part of the paper, a model presented by Philippe Martin (1999) is presented. Martin’s model combines the approaches of NEG and endogenous growth theory. In the fourth part, we develop a very simple dynamic version of the Martin model, followed by its formal analysis. We examine the effect of a monetary transfer to the poorer region, financed by the EU in the context of its cohesion policy interventions. In the fifth part, we derive some regional policy implications of the dynamised version of the Martin model. We find that there is a case for a “two step regional policy approach” in order to tackle the equity-efficiency trade-off challenge: this approach first aims to support the richer region and thus aggregate growth in the whole integrated area, and then to pursue an equity-oriented cohesion policy by fostering firm creation and innovation in the poorer region. Keywords: Equity, efficiency, trade-off, cohesion policy, regional disparities, agglomeration, growth, innovation JEL classification: R58, R11, O40, C61, C62

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1. Introduction

As is widely known, there is a general economic backwardness in Central and Eastern

European countries (CEECs) with respect to the “old” EU Member States (EU-15), due to the

legacy of the socialist era. On the other hand, the transition from centrally planned economies

to market economies and the ongoing integration with the EU have led to a strong rise of

regional inequalities within the CEECs. Hence, EU cohesion policy faces a double challenge,

and a central question of this paper is how the Union’s regional policy can contribute to attain

higher national growth (and therefore convergence towards the EU average income per

capita) and at the same time contribute to the decrease of regional disparities within the new

Member States.

The approach followed in this paper to answer this central question is a theoretical one, based

on a model framework that combines endogenous growth theory with the approach of the new

economic geography. In this context, several models have been developed to explain spatial

income inequality and to formulate possible policy strategies taking into account the equity-

efficiency trade-off. According to Martin (1998, p. 773), “[t]he new growth theory and the

new geography provide a natural conceptual framework to analyze effects of regional

policies, and to identify possible important tradeoffs between regional equity and aggregate

efficiency.” For the enlargement of the EU, as well as for future EU cohesion policy

interventions, the dynamics of this problem should be considered as fundamentally important.

This is why a dynamic version of the model presented by Martin (1999a and 1999b) is

presented in this paper, together with an effort to derive some regional economic policy

implications and recommendations.

The remainder of the paper is organised as follows: Section 2 aims at providing some

theoretical underpinnings to the problem that regional policies often face an equity-efficiency

trade-off. Section 3 outlines and analyses the model of Martin (1999a), which – in a static

way – combines new economic geography and endogenous growth theory. In particular, the

effects of a simple monetary transfer from a richer to a poorer region as well as the effects of

a regional policy targeted at innovation are examined. In Section 4, the model is extended: a

dynamic version of the model is presented, and the stability properties are scrutinised. In

Section 5, the regional policy implications of the dynamic model are examined. This section

aims at coming up with some policy recommendations for future EU cohesion policy

interventions. Section 5 also shortly concludes.

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2. Regional policies and the equity-efficiency trade-off: some theoretical underpinnings

This section examines the equity-efficiency trade-off that regional policies possibly face. In

the second half of the 1990s as well as most recently, several innovative contributions in the

literature started to combine new economic geography settings with endogenous growth

theory frameworks (e.g. Walz, 1996; Martin and Ottaviano, 1999; Martin, 1999a and 1999b).

Many of these contributions have in common that they provide a well founded theoretical

description of the trade-off between aggregate growth (on the country level) and interregional

(within-country) cohesion. Moreover, they have common precursors: some of their essential

ideas can be traced back to the “uneven development theories” of the 1950s and 1960s, whose

most prominent contributions are – inter alia – those provided by Kuznets (1955), Perroux

(1955), Myrdal (1957), Hirschman (1958), and Williamson (1965). The crucial difference is

that the new approaches managed to formalize the ideas verbally outlined already then.

2.1 The Williamson hypothesis

In an early contribution, Williamson (1965) provided a formulation of the potential trade-off

between national and regional development, predicting “increasing divergence among

geographic units within national borders and perpetuation of “pôles de croissance””

(Williamson, 1965, p. 5) in catching-up countries, whereas later during the course of

development, “instead of divergence in interregional levels of development, convergence

becomes the rule” (Williamson, 1965, p. 9). According to Williamson, the relationship

between national growth and regional inequalities takes the form of an inverted U-curve: “The

expected result is that a statistic describing regional inequality will trace out an inverted “U”

over the national growth path” (Williamson, 1965, pp. 9-10).1

Williamson’s main argument is that in the catching-up process of countries, interregional

linkages, factor movements and public policies interact in favour of growth pole effects and

the main agglomerations. Hence, more rapid growth in the growth pole areas (e.g. the capital

1 Williamson’s inverted U-shaped curve can be seen as a special Kuznets curve making reference to interregional (not interpersonal) income inequalities. Ten years before Williamson (1965), Kuznets (1955) already argued that in the early stages of a country’s development, the distribution of earnings (i.e interpersonal income inequality) widens (with labour shifting from low productivity sectors to higher productivity sectors), whereas later (when the higher productivity sector dominates the economy), income disparities narrow. The result is an inverted U-shaped curve, when growth is measured on the horizontal axis and income inequality on the vertical axis of a

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city regions) leads to an increase of regional disparities. In fact, it seems plausible that

countries at the beginning of their catching-up process prefer to promote national

development by concentrating public investment on a few growth poles, often the main

agglomerations. In these relatively early stages of catching-up, regional equity is hardly a

priority. In later stages of development, however, regional disparities may decrease due to a

higher aggregate level of income and spread effects: diseconomies of agglomeration (e.g. high

labour costs or congestion effects) may emerge in the growth poles and the lagging regions of

the by now mature country might benefit from technological diffusion and knowledge

spillovers. Moreover, the objective of spatial equity may now be given greater political

priority (Williamson, 1965, pp. 3-10; Davies and Hallet, 2002, pp. 4-5 and 9).

Most economists would probably classify the new EU Member States in Central and Eastern

Europe under the heading “catching-up countries”: hence, in Williamson’s scheme, they

would belong to the group of countries experiencing increasing regional disparities. Indeed, in

the CEECs public investment is often focused on the main agglomerations and the

maximisation of national growth (i.e. national catching-up) is mostly given priority, at the

expense of lagging, peripheral regions.

2.2 Economics of agglomeration

In the context of the model approaches integrating new economic geography and endogenous

growth theory, the most important source of a potential trade-off between regional equity

(cohesion) and aggregate growth is the often strongly positive correlation between the spatial

agglomeration of economic activities (and thus the inequality in terms of the location patterns)

and the overall growth rate. Agglomeration has countervailing effects: often positive in terms

of efficiency, but potentially negative with regard to equity (Martin, 1999a, p. 12).2

The growth benefits of agglomeration that the various strands of literature usually refer to are

general “Marshallian externalities”3, local spillovers of information, knowledge, and

graph. As mentioned before, however, Kuznets (1955) had interpersonal inequality in mind, whereas Williamson (1965) explicitly refers to the spatial dimension of development, i.e. to interregional disparities. 2 It should be emphasized that “efficiency” always denotes overall/aggregate growth, whereas “equity” can stand for interregional equity in terms of per capita income (“income equity”) as well as for equity in terms of the (then even) distribution of economic activity (“locational equity”). Hence, efficiency can be subject to a trade-off with potentially two kinds of equity. 3 “Marshallian externalities” can be traced back to a quotation by Alfred Marshall (1920, p. 225), which explains the name. Importantly, Marshallian externalities are a mixture of technological externalities (dealing with the

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technology, and economies of scale. More precisely, the formation of clusters (and thus the

move towards a potentially efficient, but uneven interregional pattern of economic activities)

is mainly due to “centripetal forces” such as the availability of specialized input services, the

formation of a highly specialized labour force, the localised accumulation of human capital,

the existence of modern infrastructure, and mass production giving rise to scale economies

(Fujita and Thisse, 2002, p. 8).

The relation between aggregate growth and regional inequality is not monocausal: on the one

hand, growth processes can trigger agglomeration dynamics and thus lead to an uneven

development within a country. On the other hand, agglomeration and regional inequality can

lead to more growth when localised technological spillovers are at play. In the model

presented by Martin and Ottaviano (2001) e.g. there is a circular causation between

(endogenous) growth and agglomeration: growth fosters agglomeration, since the expansion

of an innovative sector attracts new firms to locate in the core. At the same time,

agglomeration reduces the cost of innovation and thereby increases the growth rate in the

core. Consequently, they find that “[s]patial agglomeration of economic activities on the one

hand and economic growth on the other hand are parallel processes” (Martin and Ottaviano,

2001, p. 947).4

Seeking interregional cohesion and thus being a policy of relocation (of firms to peripheral

regions), EU cohesion policy in this context is often blamed for impeding economies from

exploiting localised intra-industry externalities and from realizing agglomeration gains

(Martin, 2002, p. 6; Midelfart, 2004, pp. 13 and 20).

Puga (2002, p. 374) speaks of “the trade-off between the economic advantages of the

clustering of activity and the inequalities it may bring.” Baldwin and Martin (2003, p. 3) point

out the “strong positive correlation between growth and geographic agglomeration of

economic activities”, which may well entail aggregate economic efficiency, but trigger spatial

effects of nonmarket interactions) and pecuniary externalities (economic interactions for which there are market and price mechanisms). This distinction goes back to Scitovsky (1954) (Fujita and Thisse, 1996, p. 345; Fujita and Thisse, 2002, pp. 7-8). 4 However – as always with theoretical results hinging on crucial assumptions – one has to be cautious and refrain from generalising both causalities: to give an example, inequality may not lead to enhanced efficiency when there are signs of over-agglomeration and congestion (Crozet and Koenig, 2004, p. 2). Yet, as the aim of this section is to give a theoretical underpinning to the equity-efficiency trade-off, dispersion or “centrifugal” forces are refrained from here, and the focus is on agglomeration or “centripetal” forces able to explain the trade-off between overall growth and spatial equity.

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disparities. Along these lines, Boldrin and Canova (2001, p. 215) emphasize that “[o]ne must

carefully distinguish between overall economic efficiency and inter-regional equality.”

2.3 The “growth pole” concept

The “growth pole” concept is very strongly related to the notion of agglomerations induced by

spillovers and economies of scale. Therefore, it shall only be examined briefly in this chapter.

In his famous “Note sur la notion de “pôle de croissance”” (“Note on the concept of growth

poles”), Perroux (1955, p. 307) observes that “[m]odels … of equally diffused growth of an

economy do not correspond to observed facts. Economic growth originates in certain zones

and proceeds with unequal intensity.” Perroux’s contribution may be considered as the

genesis of the concept of “growth poles”: it is one of the first contributions to describe how

the proximity of various economic actors leads to an intensification of economic activity, i.e.

to spatial growth agglomeration processes. These growth processes are accompanied by

increasing interregional disparities, and hence by a potential equity-efficiency trade-off

(Perroux, 1955, pp. 317-318).

Parr (1999) gets to the heart of the central idea behind growth pole strategies:

“[I]f a given level of public investment on infrastructure and inducements to the private sector could be focused within the region at a limited number of locationally favoured centres, the impact on the economy in terms of inward investment (leading to increased employment opportunities and higher per capita incomes) would be greater than under a strategy which sought to assist the least-favoured parts of the region or one which allocated expenditures on a purely proportionate basis in terms of population or employment” (Parr, 1999, p. 1200).

In fact, one can argue that the interregional allocation of public capital is efficient if it is

invested in highly productive regions (the growth poles). However, whereas this is the recipe

for a growth policy by the central government, regional policy normally (also) pursues equity

goals and thus allocates more public investment to lagging regions. If the latter are less

productive5 than the growth poles, this way of allocating capital clearly is at the expense of

5 Clearly, an important substantiation has to be added: it is important to distinguish whether “productivity” refers to the average productivity or the marginal productivity of capital and workers in a given region. Whereas the concept of marginal productivity refers to neoclassical economics, the idea of average productivity is more compatible with endogenous growth theory. What actually is the relevant criterion for determining interregional equality or disparities is a rather controversial issue (cf e.g. Sasaki, 1978; Mera, 1978) and depends on the validity and empirical relevance of the contesting growth theories. In this study, the view is taken that

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the overall growth rate and regional policy thus faces a trade-off between equity and

efficiency.

2.4 Equity, efficiency, and the case for regional policies

Trying to directly influence the allocation of resources, EU cohesion policy as carried out by

the European Commission aims at reducing the degree of agglomeration that is determined by

the market. Such a policy can only be justified on efficiency grounds if there is an allocative

market failure in the form of an over-agglomeration, i.e. if the market processes lead to too

much agglomeration (Fujita and Thisse, 1996; Südekum, 2002, pp. 130 and 132).

Hence, one has to figure out whether the degree of agglomeration is desirable from a social

welfare perspective, i.e. is there more or less spatial inequality than a “benevolent social

planner” would allow for? Hence, is there too much, too little or just the optimal degree of

agglomeration (Baldwin et al., 2003, p. 252, Pflüger and Südekum, 2004 and 2005)? Martin

and Rogers (1995) as well as Boldrin and Canova (2001, p. 215) argue that from the

perspective of endogenous growth theory and new economic geography frameworks, the

market-determined level of agglomeration is characterised by too little (not too much)

agglomeration, and hence public intervention ought to foster regional clustering and

disparities for the sake of overall efficiency.

In their model, Pflüger and Südekum (2004 and 2005) show that for high trade costs, there is

over-agglomeration in the market equilibrium (hence, regional policies should foster

dispersion, since the welfare losses of agglomeration due to congestion… are too important),

whereas for low trade costs, there is under-agglomeration.6 Consequently, policymakers

should foster the dispersion of firms only if there are high trade costs, whereas for low trade

costs, regional policies should foster agglomeration (Pflüger and Südekum, 2004, pp. 2-3).

endogenous growth theory combined with new economic geography probably describes best actual regional economics, given the frequent empirical occurrence of economies of scale, imperfect competition, and interregional differences in human capital endowments. 6 For very high and very low as well as for intermediate trade costs, the market equilibrium and the socially desirable degree of agglomeration coincide (Pflüger and Südekum, 2004, pp. 2-3).

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Trade costs can most probably be considered as low in the EU with its Single Market,

Economic and Monetary Union and deep economic integration.7 As a consequence, the EU’s

Single Market may well be characterised by under-agglomeration. Hence, EU cohesion policy

which aims at fostering dispersion in general may well be counterproductive from an

efficiency perspective. Yet, this is just an analysis on efficiency grounds. Depending on the

underlying normative objective functions, on equity grounds there may still be a case for a

policy aiming at equity in terms of an interregionally even distribution of economic activity.

So far, one important question has been neglected: after all, can the gainers compensate the

losers so that, according to the Kaldor-Hicks-criterion established in welfare theory,

everybody (including the initially lagging regions) would be (absolutely, but maybe even

relatively) better-off (Pflüger and Südekum, 2005)? In the model of Martin and Ottaviano

(1999) e.g. the “winning country’s” welfare gain from more agglomeration (in the optimal

geography than in the market-determined outcome) is big enough to make both countries

gain. Hence, the best approach seems to accept the level of agglomeration determined by the

market or even increase agglomeration, and then compensate regions/individuals that stand to

lose from this – ideally via lump-sum capitation taxes that do not entail any distortions

(Südekum, 2002, p. 132).8

However, at least three problems occur:

• Firstly, it is quite established in public finance theory that such a non-distortionary

redistribution mechanism is hardly feasible in practice. Thus, compensation payments

would have to be financed through distortionary taxes (Martin, 2000, p. 71; Südekum,

2002, p. 132). The induced distortions may well eat up the efficiency gains of

increased agglomeration.

• Secondly, even such an agglomeration-fostering and potentially welfare-improving

regional policy would still entail a trade-off between overall welfare and equity in

terms of the locational distribution of industrial activity.

• Thirdly, the approach of the European Commission’s regional policy is very different

from that of a compensatory policy: it explicitly aims at attracting economic activity to

7 Yet, they probably cannot be considered as very low or inexistent (which would entail another policy recommendation), since there are still various remaining distortions, think e.g. of the still rather limited services trade).

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peripheral regions by influencing the resource allocation. The European Commission

(2001, p. 117) itself emphasizes that its aim is to “influence factor endowment and

resource allocation … cohesion policies … are not specifically concerned … with

redistribution of income.” Hence, the Commission tries to keep production factors in

the poorer regions (or even to move them there) – clearly an equity-oriented policy,

that may come at the expense of efficiency at the pan-European level. From a growth

policy perspective, it is unwise to intervene against economic concentration in the

growth poles (Pflüger and Südekum, 2005; Südekum, 2002, pp. 133 and 138).

2.5 The equity-efficiency trade-off in models combining new economic geography and endogenous growth theory

Importantly however, even now it still cannot be concluded (neither from theory nor from the

empirical evidence) that regional policies always go hand in hand with an equity-efficiency

trade-off, even if in many cases overall growth and regional cohesion seem to be competing

goals. The reason why one shouldn’t generalise is that there is no general regional policy

approach, and one always has to distinguish between the various instruments and options for

EU cohesion policy: the latter can take the form of direct income transfers, subsidies to

producers, infrastructure investments reducing interregional or intraregional transaction costs,

education subsidies, innovation programmes…. Clearly, the existence and the extent of an

equity-efficiency trade-off depend on the instrument(s) used by EU cohesion policy and the

way the latter is implemented and financed (via distortionary taxes or lump-sum ones, via

national taxes or taxes on industrial agglomeration…) (Walz, 1996; Martin, 1999a and 1999b;

Baldwin et al., 2003; Midelfart, 2004).

Based on models combining new economic geography and endogenous growth theory, Walz

(1996), Martin (1999a and 1999b), and Baldwin et al. (2003) show that different public

policies (namely transfers, infrastructure policies and technology/innovation subsidies) have

very different effects on growth, regional income disparities and economic geography.

As shown in Section 3, in the contributions of Martin (1999a and 1999b) as well as Baldwin

et al. (2003), regional policies often face an equity-efficiency trade-off, for there is nearly

always at least one unfortunate consequence: a direct transfer/subsidy to the poor region leads

8 In this context, various authors (e.g. Franzmeyer, 2001; Südekum, 2002…) argue that EU cohesion policy should be reformed towards a fiscal equalisation mechanism based on unconditional transfers.

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to reduced regional disparities, but at the expense of the rate of innovation and hence the

country's rate of growth, which are both lowered. The same negative effect together with an

increase of regional income disparities within the country is the result of infrastructure

projects within the poorer region. When infrastructure projects aim at connecting the core and

the periphery, companies relocate to the richer region and there is thus an increase in

agglomeration. Thus, as indicated above, regional policies seem to face a trade-off between

equity and efficiency. The only exception in the cited work is a policy fostering innovation

and technology/knowledge spillovers.

Like Martin (1999a and 1999b), Walz (1996) also finds that in the case of interregional

transport infrastructure policies, the less developed regions become even more peripheralized.

Another common ground of both models: the results for the case of investment in

intraregional infrastructure (i.e. within the recipient region) are each very different from the

case of interregional infrastructure policies. Moreover, for transfers from the rich to the poor

region, Walz (1996) also finds indications for a trade-off between equity and efficiency

(which he defines as the unionwide growth rate in the economic union under scrutiny).

3. The Martin model9

The model whose assumptions, results and implications for regional policy shall be studied is

the one developed by Martin (1999a and 1999b)10: like some of the model approaches

discussed before, it “marries” an endogenous growth theory framework to a new economic

geography model.11 An important reason why we choose the approach of Martin (1999a) is

that the model with its interplay between several effects working in opposite direction (“home

market effect”, local spillovers, “competition effect”…) doesn’t lead to “circular causation”,

i.e. a core-periphery pattern as in Krugman (1991a and 1991b) or already in Myrdal (1957),

9 Section 3 is to a considerable extent based on Martin (1999a and – to a lesser extent – 1999b) and Baldwin et al. (2003), which is itself based on Martin (1999b). 10 The essay “Are European regional policies delivering?” (Martin, 1999a) won the First Prize in the EIB Prize essay competition of the European Investment Bank (EIB). Martin’s article “Public policies, regional inequalities and growth”, which has been published in the Journal of Public Economics (Martin, 1999b), features the same model approach, yet in a more analytical form. The same is true for Chapter 17 of Baldwin et al. (2003), for which Martin’s studies have served as a basis. For the study here, the EIB Prize winning essay is chosen as the main basis, since it is more straightforward and intuitive (whereas the mathematics would not yield much added value for the aims pursued here), and since the simpler model is a more suitable basis for the dynamisation approach followed in Section 4. 11 The model of Martin (1999a and 1999b) is based on previous work by Martin and Rogers (1995) and Martin and Ottaviano (1999). The endogenous growth framework follows Romer (1990) and Grossman and Helpman (1991). The endogenous geography is introduced in a similar way as in Helpman and Krugman (1985) and Krugman (1991a).

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where all firms will decide to produce only in the richer region. The aforementioned effects

and the freely moving endogenous capital in Martin’s model lead to interior solution

equilibria, in which production takes place in both regions, generally in an uneven spatial

pattern. This clearly increases the relevance for the discussion of regional policy implications.

3.1 The assumptions, variables, and the relationship between growth, regional income disparities and agglomeration

Martin’s model features two regions: a capital-rich region and a relatively poor one. If we

apply this structure to the case of Hungary e.g., we could think of Budapest as the former and

of Eastern Hungary as the latter. Transaction costs exist between regions as well as within

regions, and they are affected by public infrastructure policies. As is often the case in models

combining new economic geography and endogenous growth theory, there is a homogeneous

(“traditional”) good and a composite (“differentiated”) good. The production of the latter

takes place under monopolistic competition and involves economies of scale (as in Dixit and

Stiglitz, 1977). The model is then elaborated on the basis of three theses.

Thesis 1: When transaction costs between the regions are reduced, the spatial concentration of

firms in the rich region increases, since it always pays off to produce in the richer area, where

economies of scale can be maximised, while sales to the poor region can continue, thanks to

reduced transaction costs. When regional income disparities increase, the agglomeration

degree also increases: because of economies of scale, firms always locate where demand and

income are highest. This effect is the so-called “home market effect”. The resulting

equilibrium relationship (with firms’ profits eventually being equal in both regions) is

( )A A R= , with ( )' 0A R > , (1)

where A is an agglomeration index, and R is an index of regional income inequality.

Thesis 2: As agglomeration (in the richer region) increases, the cost of innovation falls in the

richer region, due to the aforementioned (localised) spillovers of information, knowledge and

technology. Hence, an increase of spatial concentration leads to an increase of innovation and

consequently to an increase in the (aggregate) growth rate. This is the so-called “spillovers

effect”. The equilibrium relationship (between agglomeration and long-term growth) is

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( )g g A= , with ( )' 0g A > , (2)

where g is the rate of growth (and the rate of innovation).

Thesis 3: A high rate of innovation leads to more market entries by new firms, which compete

with incumbent firms and reduce their profits and thus existing incomes. As monopolistic

firms are more numerous in the rich region than in the poor region, the decline of their profits

leads to a reduction of regional income disparities. The respective effect could be called

“competition effect”. The respective equilibrium relationship is:

( )R R g= , with ( )' 0R g < (3)

If theses 2 and 3 are summed up, the following relationship is obtained:

( )( ) ( )R R g A R A= = , with

( )' 0R A <

(4)

Figure 2: The relationship between growth, regional income disparities and agglomeration

Source: Martin (1999a, p. 14).

Agglomeration

AA

Regional income disparities

Innovation and growth rate

RR

SS

A

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Figure 2 sums up Equations 1 to 4, i.e. the respective equilibrium relationships. The

intersection of the two curves AA and RR in Figure 2 denotes the equilibrium levels of

agglomeration and income inequality. The equilibrium rate of innovation is indicated by the

intersection of the line A (which stands for the equilibrium level of agglomeration) with the

curve SS (the latter’s positive slope shows the positive relation between agglomeration and

innovation/growth).

Now the effects of various types of regional policies shall be examined in the theoretical

framework provided by Martin (1999a).

3.2 The effects of income transfers and regional policies targeted at innovation

Figure 3: The effects of an income transfer to the poor region

Source: Martin (1999a, p. 17).

The initial impact of a simple monetary transfer from the rich to the poor region (e.g. from

Budapest to Eastern Hungary) is to decrease regional income inequality. Hence, in Figure 3,

the curve RR shifts downwards/to the left. As a consequence, the extent of agglomeration will

be reduced. Thus, there is a move along the AA curve to the left. This is not surprising, since

the transfer of purchasing power to the poor region increases the market size there and attracts

firms to the poor region. The more dispersed economic geography following the decrease of

Agglomeration

AA

Regional income disparities

Innovation and growth rate

RR

RR’

SS

A

A’

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agglomeration however is less conducive to spillovers and thus innovation and growth are

lowered. Summing up, regional disparities and inequalities in terms of industrial location

become less unequal (both equity goals are thus achieved), but at the expense of overall

efficiency. There is an equity-efficiency trade-off.

( ) ( ) ( )R g A R g A!" !" ! . (5)

The decisive question is: Is there an approach to regional policy able to contribute

simultaneously to higher growth and spatial equity? As can be seen from Figure 4, in contrast

to the “traditional” transfer policies, a policy aimed at reducing regulatory barriers to

innovation or the costs of innovation, makes it possible simultaneously to achieve objectives

of reducing agglomeration, regional inequalities, and increasing the rate of innovation/growth.

The regional policies involved could be information and communication infrastructures, R&D

subsidies, education infrastructure (i.e. human capital, which is a conditio sine qua non for

innovation and technology adoption) or making capital markets more conducive to new start-

ups.

( ) ( ) ( )g A R g A R!" #" # . (8)

Figure 4: The effects of a regional policy fostering innovation and technology spillovers

Source: Martin (1999a, p. 19).

Agglomeration

AA

Regional income disparities

Innovation and growth rate

RR’

SS

A’

A

AA’

SS’

RR

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Suppose that the policymaker reduces the cost of innovation by facilitating its diffusion, e.g.

by improving information and communication infrastructures, which makes it easier for

lagging regions to innovate and to adopt new technologies. Obviously, with the cost of

innovation being reduced, the growth rate increases (SS becomes SS’ in Figure 4). More firms

enter the market, which boosts competition, reduces the profits of monopolistic businesses

(which are more numerous in the rich region than in the poor region) and ultimately the

income disparities between the capital city and its periphery (we move from RR to RR’). As a

consequence, agglomeration is reduced, too (a move to the left along the curve AA).

The “secret” behind the regional policy approach fostering innovation or knowledge

spillovers is that it makes the localised spillovers that are built in the model less localised. As

Baldwin et al. (2003, p. 433) put it, “making knowledge spillovers more global is both pro-

growth and pro-dispersion”, since on the one hand, the lagging regions benefit more from

spillovers, and this increases the growth rate of the aggregate space (e.g. the whole country of

Hungary).

As mentioned above, possible policy approaches in this context could include policies that

improve telecommunication and IT infrastructures or the human capital base in the lagging

region (thus enabling technology transfer). Again, to follow Baldwin et al. (2003, p. 433),

“[o]ne could think of this type of policy as one that facilitates trade in ideas rather than trade

in goods.” Hence, this innovative approach focuses on the removal or reduction of transaction

costs on ideas and technologies, not on the traditional elimination of transaction costs on

goods. It is important to emphasize that any policy able to reduce the cost of innovation may

yield the desirable outcomes sketched in Figure 4. Hence, the respective policy could also be

an R&D subsidy or a policy improving the education infrastructure or increasing competition.

4. Adding dynamics to Martin’s model

Although Martin (1999a) in his line of reasoning mentions several times the process-related

character of the results of his model, he doesn’t take into account the time dependency of the

variables. Instead, he contents himself with a comparative analysis of the initial points and

end points in equilibrium. In this section, we address the dynamics of Martin’s model in the

framework of a simple model.

16

Indeed, a major difference to Martin’s line of reasoning follows from the dynamic method of

analysis – as opposed to Martin’s static approach. In the original model, Martin (1999a) in a

sense can/has to emanate from institutionally given income disparities, whose extent changes

due to economic policy interventions, whereas the dynamic approach requires the

specification of an own pathway of the evolution of regional income disparities over time.

4.1 A dynamic version of Martin’s model

We continue examining two regions of an integrated area – a capital-rich region, and a

relatively poor region. The former has a higher degree of agglomeration than the latter. The

regional incomes should not be understood in terms of the earnings obtained, but in terms of

variables which are different from the earnings obtained due to economic policy interventions.

tN is the number of firms in the integrated area at time t . These companies proliferate at a

constant rate Ng .12 The number of firms located in the richer region at time t is A

tN , with

t

A

tNN < ; consequently, the number of firms in the in the poorer region is A

ttNN ! . The

expression t

A

t

N

N is an indicator for the degree of agglomeration (remember Martin’s

agglomeration index A , Eq. (1) and Martin, 1999a, pp. 12-13). Hence, t

A

t

t

N

NA = . The growth

rate of the degree of agglomeration is thus

AA NN

g g g= ! , (9)

or, respectively,

t

t

A

t

A

t

t

t

N

N

N

N

A

A &&&!= .

(10)

12 This somewhat unrealistic assumption can be refrained from without major difficulty: it could be assumed e.g. that the number of firms evolves along a logistic function, i.e. that the aforementioned growth rate instead of the constant value

Ng takes the form

Ng nN! , where n is a positive number. This wouldn’t alter essentially the

following comments.

17

Furthermore, Ay is the income of a firm in the rich region. Hence, the income of that region is

given by AANy . If the aggregate income of the integrated area at time t is

tY , then the income

share of the richer region at time t is given by t

A

t

A

t

Y

Ny . In the model of Martin, the

corresponding index is R , the index of inequality of regional incomes (Eq. (1) and (3) and

Martin, 1999a, p. 13). Here, t

A

t

A

tt

Y

NyR = . Consequently, the growth rate of regional income

disparities is given by

t

t

A

t

A

t

A

t

A

t

t

t

Y

Y

N

N

y

y

R

R &&&&!+= .

(11)

It is central to Martin’s model that the growth rate of income is a growing function of the

degree of agglomeration (Eq. (2) and Martin, 1999a, p. 13). This relationship shall be given

by

( )tA

t

A

t Afy

y=

&, mit ( ) 0>!f .

(12)

Eq. (11) and (12) together result in

( )

t

t

A

t

A

tt

t

t

Y

Y

N

NAf

R

R &&&!+= .

(13)

The income of the poorer region can be expressed as ( )tt

A

t

A

tt RYNyY !=! 1 . One part of this

income is used to develop that region, i.e. measures are taken that promote the creation of

firms in the poorer region or the relocation of firms from the richer to the poorer region. The

other part of the income is used for the consumption of goods that are produced in the richer

region. This stimulates production in the richer region, thereby leading to a growing number

of firms. The share of income of the poorer region which is used to buy goods produced in the

other region shall be given by ( )ttRY !1" , with ! being subject to economic policy

interventions. Apart from the poorer region’s consumption of goods produced in the richer

region, another variable influences the number of firms in the richer region: the local demand

18

in the richer region, which can be expressed as A

t

A

t

ANy! , with A! being the richer region’s

propensity to consume. Regarding the relation between ! and A! , we assume that A!! > .13

Hence, the number of firms in the richer region changes according to:

( )( ) ( )( )1 1A A A A A

t t t t t t t t tN h Y R y N h Y R RY! ! ! != " + = " +& ,14 (14)

where h is linear homogeneous in tY and ( ) 0h! > .

Consequently, the growth rate of firms in the richer region is

( )( )1AA

t t tt

A A

t t

Y h R RN

N N

! !" +=

&.

(15)

With this result, the growth rate of the degree of agglomeration is

( )( )1A

t t ttNA

t t

Y h R RAg

A N

! !" += "

&.

(16)

Equations (13) and (16) describe the dynamics of the two regions within the integrated area

through the variables tA and

tR . If, for the sake of simplicity, we assume constant labour

productivity for the richer region, then kN

Y

A

t

t = and thus t

t

A

t

A

t

Y

Y

N

N &&= . If we assume furthermore

– also for the sake of simplicity – that ( )h is a constant and both ( )h and ( )tAf are linear

functions, then Eq. (13) and (16) yield the following expressions:

13 This reflects the fact that the poorer region hardly produces any higher value-added products on its own. Hence, it is obliged to import those from the richer region. This approach corresponds to the conditions prevalent in the literature, i.e. that both regions produce agricultural products, but manufactured goods are only produced in the richer region (cf e.g. Martin and Ottaviano, 2001; Ottaviano, Tabuchi, and Thisse, 2002). Araujo and Teixeira (2004) argue that “Southern” countries typically produce and export primary (i.e. agricultural) goods, whereas “Northern” countries typically produce and export industrial (i.e. manufactured) goods. In this context, the South (the “poor region”) heavily depends on Northern (the “rich region’s”) capital goods. The relatively lower income elasticity of demand for agricultural products is seen as one of the main reasons for the declining share of consumer expenditures on Southern goods, and thus for international/interregional inequalities. 14 The function ( )h describes the reaction rate of firm creation or firm closure in the richer region when

demand changes.

19

t

t

tA

R

R

10!! +"=

&, 0,

10>!! ,15

(17)

and

( )( ) ( ) t

A

NNt

A

t

t

t khRgkhgRRkhA

A!!!!! "+"="+"= 1

&.

(18)

The stationary equilibrium is given by

1

0

!

!=

"A (19)

and

kh

khgR

A

N

)( !!

!

"

"=

# . (20)

For the index of inequality of regional incomes, the following must hold: 10 !!tR . From

Eq. (20), it can be seen that the regional income distribution depends on labour productivity,

since 0=R , if !h

gk N= ; respectively, 1=R , if

A

N

h

gk

!= . As A!! > holds, the

nonnegativity of !R is only assured if !khgN < .

In order to analyse the stability properties of the equilibrium solution, we look at the Jacobian

matrix

( )1

0

1

0( )

,

( ) 0

N

A

A

g kh

khJ R A

kh

!"

! !

"! !

"

# #

$% &' ($' (=' (

$' () *

,

(21)

15 Eq. (17) is based upon the realistic premise that regional income disparities decrease when there is no agglomeration, i.e. when production is equally distributed among the two regions.

20

whose eigenvalues can be calculated from the equation

( )!"# khgN $=0

2 . (22)

From Eq. (17), the stability properties of the model are immediately apparent: Since, due to

the condition 0R ! , the relation Ng kh!< holds, the discriminant is negative, i.e. Eq. (17)

has two conjugated complex solutions; the real parts of 1! und

2! are 0. Hence, the stationary

soluation is instable.16

Hence, if labour productivity is sufficiently high, agglomeration and regional disparities

evolve along regular though phase-delayed cycles (Figure 5a), whose periods’ length then –

provided that firm creation is decreasing or stagnating in the whole integrated area - takes the

values of 0

2

kh

!

" # and, respectively,

( )0

2

Ng kh

!

" #$ (Hirsch and Smale, 1974, p. 95).

Hence, the length of the periods depends on

• average labour productivity,

• the flexibility of firm creation or firm closure with changing demand,

• the demand of the lagging region for goods that are produced in the richer region, and

• the (falling) growth rate of income disparities between both regions.

Clearly, the opposite evolution of the parameters just examined would lead to a shortening of

the periods.

The relationships derived lead us to the conclusion that the exclusive stimulation of the

creation of new firms17 is not a guarantee for a stable development in the regions. The

decisive variable is the degree of labour productivity that is reached (or can be reached) in the

richer region. Yet, even then there can be at best a phase-delayed, cyclical evolution of the

examined variables.

16 If this condition is fulfilled, the model is a Lotka-Volterra model (cf e.g. Assenmacher, 1990). 17 Regarding the transition process in the CEECs, we could also say: the disintegration of the former big public monopoly firms and their transformation into smaller units.

21

Figure 5a: The evolution of agglomeration and regional disparities over time )(),( tAtR

t

!A

maxA

minA

minR

maxR

!R

Regional income

disparities

Degree of agglomeration

4.2. The effects of EU cohesion policy income transfers in a dynamic context

In his study, Martin (1999a) examines – inter alia – the implications of monetary transfers for

regional development. In his line of reasoning, simple monetary transfers from the richer to

the poorer regions lead to a decrease of regional income disparities (Martin, 1999a, pp. 16-

17). In contrast to Martin’s line of reasoning, we do not assume a transfer from the richer to

the poorer region, but an “exogenous” transfer from a third party – in practice, this would be

the European Union/European Commission, who spends billions of euros annually for its

cohesion policy interventions in the EU’s poorest regions.18 Also in contrast to Martin’s line

of reasoning, these transfers shall not lead directly to a decrease of regional income

disparities, but shall be placed at the disposal of the economic agents of the poorer regions,

who can buy (mainly manufactured) goods with them.19

18 One could e.g. assume a transfer from Brussels to Eastern Hungary (Hungary’s poor region), which has significant effects on Hungary’s rich region, Budapest, too. 19 In the present dynamic version of the model, it would not make much sense to assume a policy directly influencing regional income disparities, since we presumed that regional income disparities vanish nearly automatically if there is no agglomeration. Consequently, the more adequate policy approach is one targeted at a decrease of the degree of agglomeration.

22

Let us assume that m denotes the monetary transfer. Consequently, the disposable income in

the poorer region increases to A A

t t tY m y N+ ! . If we further assume that the monetary transfers

depend on the aggregate income of the whole integrated area, i.e. that t

m Y!= (with

0 1!< < ), then the poorer region’s demand for goods produced in the richer region changes

to ( )1tR! "+ # . This makes the dynamics of the degree of agglomeration change. Instead of

Eq. (18), we now have

( )( ) ( ) t

A

NNt

A

t

t

t khRgkhgRRkhA

A!!"!!"! #+#+=#+#+= )1(1

&

.

(23)

The determinants of the growth rate of regional income disparities remain unchanged. The

new model is thus given by Eq. (17) and (23). The respective stationary solutions are

1

0

!

!=

"A

(24)

and

kh

khgR

A

N

)(

)1(1

!!

"!

#

+#=

$

.

(25)

Since however A! !> , in order to assure the positivity of R! , the condition (1 ) Nkh g! "+ >

has to be fulfilled, and this is easily the case. Yet, then 1R R! !> , because (1 )kh kh! " !+ > .

Hence, the intervention via transfer payments aiming at reducing regional income disparities

leads to the contrary: regional inequality and the growth rate of agglomeration increase. The

latter does so since ( )( ) ( )( )1 1A A

t t N t t Nkh R R g kh R R g! " ! ! !+ # + # > # + # (cf. Eq. (18)

and (23)). Thus, the opposite policy approach would seem to be promising if interregional

cohesion is the main goal. Even if it is an idle question if the lagging region should be extra-

taxed, the basic conclusion remains: an income support to the lagging region doesn’t yield the

desired outcome.

23

The reason for this seemingly counter-intuitive result is the way demand is “steered”: the

increased disposable income in the lagging region leads to increased demand, which is

satisfied by enhanced production in the richer region. The result is a higher income in the

latter, which ultimately leads to an increase of regional income disparities. This confirms the

occurrence of an equity-efficiency trade-off that is also prevalent in the original Martin

model, according to which transfers from the rich to the poor region lead to reduced income

disparities and to a reduced degree of agglomeration and thus to less innovation and growth.

Hence, in both versions of Martin’s model (static and dynamic), a simple monetary transfer to

the poorer region (no matter if it comes from the richer region or from the EU) involves an

equity-efficiency trade-off. However, this trade-off has a different sign in the two cases: while

in Martin’s static context, the outcome is compatible with the equity goals, but fails to pass

the efficiency test, the result in the dynamic context (and with an EU transfer) is an efficient

policy enhancing overall growth, but at the expense of equity (both in terms of income and

location).

If we examine the stability properties of the stationary solution, we find that the monetary

transfer doesn’t entail any qualitative changes. The Jacobian matrix now has the form

( )1

0

1

(1 )0

( ),

( ) 0

N

A

A

g kh

khJ R A

kh

! "#

! !

#! !

#

$ $

% +& '( )%( )=( )

%( )* +

,

(26)

with the eigenvalues

[ ])1(0

2 !"#$ +%= khgN . (27)

The solutions are again conjugated complex, thus our earlier statements regarding the

evolution of the degree of agglomeration and the regional income disparities in the

neighbourhood of the equilibrium remain valid.

However, there is a difference with regard to the length of the period, which now takes the

value [ ]0

2

(1 )Ng kh

!

" # $% +. The expression in (square) brackets has increased compared to

24

the situation without transfer payments, i.e. the regular cycles are shortened due to the transfer

payments.

5. Policy implications and conclusion

As we have shown in Chapter 4.2, the effect of an EU transfer (e.g. in the context of the

Union’s cohesion policy) to the poorer region interestingly is to particularly increase income

in the richer region, since the poorer region’s transfer-induced additional demand for

manufactured goods can only be satisfied in the richer region. This additional demand

increases firm creation and agglomeration in the richer region, and thus the rich region’s

income (in line with Eq. (14), (15), and (23)). Ultimately (and absolutely), both regions gain:

the richer region because of increasing incomes, and the poorer region because it can satisfy

its demand for manufactured goods from the richer region better than in the situation before

the transfer. Yet, in terms of the location/creation of firms as well as in terms of income, the

richer region stands to gain much more from this EU regional policy intervention than the

poor region. Hence, relatively speaking, the poorer region falls behind even further. Though

the policy is efficient (for it increases aggregate growth in the integrated area), it is

counterproductive if interregional cohesion is the main objective, given that the interregional

differences with regard to firm location and income increase even more. What may be the

policy response to tackle this equity-efficiency trade-off?

In this paper, we suggest a “two-step regional policy approach”: Figure 5b illustrates once

more the cyclical evolution of regional disparities and agglomeration. EU cohesion policy

should not try to counteract or reverse these cycles, but try to use them and benefit from them

in order to stimulate overall efficiency in a first step and interregional equity in a second step.

The first step that ought to be recommended to EU cohesion policymakers is to promote

overall growth in the integrated area and in the richer region, which should act as the dynamo

of growth – last but not least via transfers to the poor region, which stimulate demand for

manufactured goods to be satisfied in the rich region, increasing firm creation and income

there, while the poorer regions’ consumers better can satisfy their needs thanks to the

transfers. In terms of Figure 5b, this first step should be pursued up until Points 1a and 1b are

reached, i.e. as long as agglomeration and the growth rate of regional disparities increase

anyway. Before turning to an equity-oriented policy, the main objective of this efficiency-

oriented first step is to “make the pie as big as possible, before cutting it into slices”.

25

Figure 5b: The evolution of agglomeration and regional disparities over time: the policy implications

1a

Regional income

disparities

1b

2

)(),( tAtR

t

!A

maxA

minA

minR

maxR

!R

Degree of agglomeration

Point 1a is an inflexion point of the regional disparities curve: from there onwards, the growth

rate of regional disparities decreases, before turning negative in Point 2. Moreover, from Point

1b onwards, the degree of agglomeration decreases. Hence, from Points 1a and 1b onwards,

regional policymakers ought to give way to an equity-oriented policy, in order to enhance

cohesion between the richer and the poorer region. This could be done by fostering the

creation of innovative companies in the poorer region, so that A

ttNN ! increases. Thereby,

( )tt

A

t

A

tt RYNyY !=! 1 , i.e. the income of the poorer region, increases, too. While

agglomeration and regional disparities are reduced, the poorer region now gets an increasing

share of the pie – a pie whose size has been increased by the first step of the policy approach.

The more these newly created companies in the poor region are able to benefit from spillovers

and knowledge/technology transfer (particularly from companies in the richer region), the

more productive they will be, and the more efficient the overall policy will be – apart from

being equity-oriented, which is the main objective in this second phase. Ideally, this second

step policy even entails efficiency gains (which is the case if the firms newly founded in the

poorer region are more productive than those in the rich region (cf Footnote 5)). Hence, there

clearly seems to be a case for a regional policy targeted at the transfer of innovation,

technology and knowledge to the poorer region in this second step of a two-step regional

26

policy – instead of the monetary transfer that dominated the first step. This innovation-

oriented policy clearly resembles the policy advocated by Martin (1999a, pp. 20-21), who

argues for policies that “would have the objective of increasing the capacity of poor regions to

absorb new technologies and to increase spatial diffusion of innovation.”

Clearly, our “two step regional policy approach” combines what growth pole concepts (cf

Chapter 2.3) aspire to achieve: first enhance growth in a favoured centre, and then build on

spread effects starting from this centre, favouring the periphery and thus leading to

interregional cohesion. The problem of most growth pole concepts is that they do not deliver a

policy recipe for this second part of the story: typically, spread effects are assumed (to fall

like “manna from heaven”), but there is no concrete strategy in case they don’t materialise –

an example are the new German Bundesländer, where the existing growth poles are still too

weak to make up for spread effects: consequently, the periphery does not grow, and

development remains concentrated in a very limited number of growth poles.

Another advantage of the “two step regional policy approach” is that it solves one of the main

problems due to the political economy of regional policy: governments always feel a strong

pressure “to be seen to be doing something for the less-favoured regions” (Parr, 1999, p.

1206). Hirschman (1958, p. 190) already argues that the most pervasive tendency of

governments is “the dispersal of funds among a large number of small projects scattered

widely over the national territory”. Governments thus often ignore the more efficient part of

regional policy – to support the dynamos of growth. In the “two step regional policy

approach”, this important aspect is duly taken into account: first the growth poles are favoured

(something that may be politically difficult to push through), and only then – when the basis

for an equity-oriented policy is created – a clearly equity-oriented regional policy is pursued,

fostering firm creation based on innovation spillovers and knowledge transfer.

27

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horizontaler Finanzausgleich aus allokativer Sicht erforderlich?’ VI Okruch, Stefan. 2003. „Evolutorische Ökonomik und Ordnungspolitik – ein neuer

Anlauf”. VII Meyer, Dietmar: „Humankapital und EU-Beitritt – Überlegungen anhand eines

Duopolmodells.” VIII Okruch, Stefan. 2003. „Verfassungswahl und Verfassungswandel aus ökonomischer

Perspektive - oder: Grenzen der konstitutionenökonomischen Suche nach der guten Verfassung.”

IX Arnold, Volker – Hübner, Marion. 2004. „Repression oder Umverteilung - Welches ist

der beste Weg zur Erhaltung der Funktionsfähigkeit marktwirtschaftlicher Systeme? - Ein Beitrag zur Theorie der Einkommensumverteilung.”

X Bartscher, Thomas, Ralph Baur and Klaus Beckmann. 2004 „Strategische Probleme

des Mittelstands in Niederbayern”

XI Alfred, Endres. 2004 „Natürliche Ressourcen und nachhaltige Entwicklung” XII Chiovini, Rita and Zsuzsanna Vetõ. 2004. „Daten und Bemerkungen zu den

Disparitäten im Entwicklungsstand ausgewählter Länder” XIII Meyer, Dietmar – Lackenbauer, Jörg. 2005 „EU Cohesion Policy and the Equity-

Efficiency Trade-Off: Adding Dynamics to Martin’s Model” Paper copies can be ordered from:

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